32 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



the quantities a w0 and o- m being calculated as explained above from the formulae 01 

 the tables of Martin Knudsen. Mr. Ekman's discussion of his results shows that 

 the specific volume calculated by the formula will not probably contain greater 

 error than o.ooooi for the pressure of iooo d-bars, and proportionally o.oooi for 

 10,000 d-bars. Still more important for the oceanic dynamics is the following con- 

 clusion from Mr. Ekman's discussion: Differences in the specific volume of two 

 samples of sea-water taken from the same depth, which have been calculated by this 

 formula, will be perfectly reliable in the fifth decimal in all cases met with in 

 the sea. 



27. Tables for the Specific Volume of Sea-Water. We shall never use the 

 preceding formulae directly in investigations in statics or dynamics of the sea. They 

 will only serve for the construction of tables giving the specific volume or the 

 density of sea-water for all necessary values of the independent variables. This 

 tabulation, however, contains difficulties. The greatest depth hitherto sounded in 

 the sea being 9636 meters, the sea-pressure can vary from o to about 10,000 d-bars. 

 The temperature can vary from 2 to about 30 C. and the salinity from o to about 

 4o/ 00 - Modern observations being taken with a precision of about 0.01 C. and 

 of 0.0 1 / 00 of salinity, the tables should not have greater intervals than 0.1 C. 

 and 0.1 /oo salinity. To be able to interpolate conveniently to any depth, the pres- 

 sure should not be taken with greater intervals than 10 d-bars. The direct tabu- 

 lation would thus involve the calculation of 320 X 400 X 1000 = 128,000,000 

 different values of the specific volume. By printing 500 numbers on each page the 

 tables would cover 256,000 pages. The direct tabulation must thus be given up, 

 and we shall have to use in a more developed form the principles exemplified for 

 the case of two variables in tables 3 m to 6 m and 3 h to 6 h, viz, to break up the 

 quantity to be tabulated in a sum of terms, each of which is more easily subject to 

 tabulation. 



To carry this through in the present case, we can use a development analogous 

 to that of Taylor. We first write 



(a) a ,r P = a 35, 0, ,, + 8 



Here a 35 ,o,,, denotes the specific volume of sea-water of the constant salinity 35 /oo 

 and the constant temperature o C. under any pressure p. These special values of 

 salinity and temperature are not very far from the average values in the deep 

 oceans, and we shall therefore denote a^j^as the normal specific volume of the sea- 

 water under the pressure p. The value a 3rp representing the specific volume of 

 any kind of sea-water under the same pressure p is then found from a^, i0iP by the 

 addition of a correction 8, which we shall call the anomaly of the specific volume 

 This correction will be a function of salinity, temperature, and pressure, and can be 

 broken up in a series of terms 



(b) 8 - 8, 4- K + S ST + S v + B Tp + S STP 



where the indices show the variables upon which the different terms depend. 



